You board when you board. Access in Seattle on the Diamond is not great but the cruise staff will assist you. My mother-in-law needs a wheelchair and they helped her getting on/off at every port. As the Diamond Princess is not an american flag vessel (as with all other Princess ships too) there not required by law to comply with the U.S. ADA laws.
We just returned from the Sapphire Princess, and WC people do get ahead of some others. When we first got on, we did wait in a shorter line because my mom used one of their WC's to enter. It is a very long up ramp to embark. The staff was very helpful to people in WC';s.